UPSC NDA Math Model Paper 6

For statement (1),
Put point (0, 4, 0) in equation of the circle,
0+42+0+0+2(−2)(4)+0=0
⇒ 16 - 16 = 0
⇒ 0 = 0
∴ the circle passes through (0, 4, 0)
Hence, statement (1) is correct.
For, statement (2),
Distance between (1, 1, 1) and (-1, 2, -3) is given as,
=√(1−(−1))2+(1−2)2+(1−(−3))2
=√4+1+16
=√21 Hence, statement (2) is incorrect.